Automatic Weights not recalculating after moving Bone
I believe you should be in edit mode and not pose mode.

Suggestion. Manual weight painting is time costly.  If you have zero or or close to zero investment in manual weight painting then simply delete your existing [bone weight] work and start fresh to be time effective.  You have the luxury at the moment of discarding what might be a mistake rather than doing a sequence of recovery steps.

Simply assign automatic weights all over again.  That is 8 seconds of work. In your situation, the action of 

Parent Armature with automatic weights Control-P

can be done many times since you are not losing time costly manual weight painting.

Please know that a large bone next to a small bone will have generally more influence except where the small bone is extremely close to the mesh.